codechef Sums in a Triangle題解

Let's consider a triangle of numbers in which a number appears in the first line, two numbers appear in the second line, three in the third line, etc. Develop a program which will compute the largest of the sums of numbers that appear on the paths starting from the top towards the base, so that:

• on each path the next number is located on the row below, more precisely either directly below or below and one place to the right;
• the number of rows is strictly positive, but less than 100
• all numbers are positive integers between O and 99.

  Input

  In the first line integer n - the number of test cases (equal to about 1000).
  Then n test cases follow. Each test case starts with the number of lines which is followed by their content.

  Output

  For each test case write the determined value in a separate line.

  Example

  Input:
  2
  3
  1
  2 1
  1 2 3
  4 
  1 
  1 2 
  4 1 2
  2 3 1 1 
  
  Output:
  5
  9

  
  

  使用動態規劃法解決本題。

  和一題leetcode題一樣，從底往上查找路徑。

  
  

  #include 
  #include 
  #include 
  #include 
  #include 
  using namespace std;
  
  int triPath(vector > &tri)
  {
  	if (tri.empty()) return 0;
  	vector path(tri.back());
  	for (int i = (int)tri.size() - 2; i >= 0 ; i--)//unsigned做減法會溢出！！！
  	{
  		for (int j = 0; j < (int)tri[i].size(); j++)
  		{
  			path[j] = max(path[j], path[j+1]) + tri[i][j];
  		}
  	}
  	return path.front();
  }
  
  int SumsinATriangle()
  {
  	int T, n;
  	scanf("%d", &T);
  	while (T--)
  	{
  		scanf("%d", &n);
  		vector > tri;
  		for (int i = 1; i <= n; i++)
  		{
  			vector tmp(i);
  			for (int j = 0; j < i; j++)
  			{
  				scanf("%d", &tmp[j]);
  			}
  			tri.push_back(tmp);
  		}
  		printf("%d\n", triPath(tri));
  	}
  	return 0;
  }